Are we talking indirect routings for mileage runs or indirect routings for travel you actually had to take for non-MR purposes? Big difference between those two scenarios.
Not counting MRs, some that come to mind for me:
DFW-MSP-ATL-SJU (Wanted to fly DL, not AA, and the double-connect via MSP & ATL was cheaper than a single connect over ATL)
DFW-SAT-DFW-SEA (Cheaper to combine a DFW-SAT OW with a SAT-SEA OW than to fly nonstop DFW-SEA)
HPN-ATL-DFW-SLC-LAS (Already had LAS vacation booked but had client business in HPN pop up on short notice. Easier to just combine existing DFW-LAS booking with new HPN-DFW ticket)